Question

. 7:08 < MTHM 168 Common F... Q Problem f_Wae the following terms al-Arecent study shows that just one session of te behavioral therapy can help people with insomnia. In the study forty people who had been diagnosed with were randomly divided into two pups of 20 each. People in one group received one hour behavioral therapy session while those in the other group received no treatment. Three months later, 310 hose in the therapy group reported sleep improvements while only people in the other group reported improvements Improvement No improvement Therapy 7 20 5 Total # B points) Le pr-the proportion of the people receiving therapy that reported sleepingrovements and #the proportion of people who did not receive therapy that reported improvements Calculate - Show your work points in testing to see if there is evidence that people receiving cognitive behavioral therapy experience greater sie improvements than those who do not recewhat are the land me hypotheses! Uue proper notation Ne (4 points A randomization distribution for this test is pictured below. Use the fact that there are 200 den the distribution to estimate the prale. Justify your answer Justification: 4(points Use your pale from port to make a decision and conclusion about these hoes De to word your conclusion in the content of the problem D Dashboard Calendar To Do Notifications Inbox

Answer 1

(a) pT = 13/20 = 0.65

pN = 5/20 = 0.25

pT - pN = 0.65 - 0.25 = 0.4

(b) The hypothesis being tested is:

H₀: p₁ = p₂

H_a: p₁ > p₂

(c) z = 0.4/0.154 = 2.60

p-value = 0.0047

Since the p-value (0.0047) is less than the significance level (0.05), we can reject the null hypothesis.

(d) Therefore, we can conclude that people receiving cognitive behavioral therapy experience greater sleep improvements than those who do not receive therapy.